We define the electric and gravitational fields as \begin{eqnarray*} \gv &=& -\grad \Phi \\ \EE &=& -\grad V \end{eqnarray*} Masses and (positive) test charges will move in the direction of the corresponding field, that is, in the direction in which the potential decreases.

The electric field at the point $\rr$ due to a point charge at the origin is \begin{eqnarray*} \EE = \frac{1}{4\pi\epsilon_0} \frac{Q\,\rhat}{r^2} \end{eqnarray*} (What coordinates are being used here?) A coordinate-independent expression for $\EE$ can be obtained by realizing that $\rr=r\,\rhat$, resulting in \begin{eqnarray*} \EE = \frac{1}{4\pi\epsilon_0} \frac{Q\,\rr}{|\rr|^3} \end{eqnarray*} These expressions can also be derived by differentiating $V$.